Why QC Rewards Technique Over Calculation
Quantitative Comparison (QC) questions ask you to compare Quantity A and Quantity B, not to compute an exact final value. Test-takers who fully solve both sides every time waste precious minutes; test-takers who simplify and compare directly finish faster and make fewer errors.
Quantitative Comparison (QC) প্রশ্নে Quantity A ও B-এর তুলনা করতে হয়, নির্দিষ্ট চূড়ান্ত মান বের করতে হয় না। যারা প্রতিবার সম্পূর্ণ সমাধান করেন তারা সময় নষ্ট করেন; যারা সরলীকরণ করে তুলনা করেন তারা দ্রুত ও নির্ভুলভাবে শেষ করেন।
The core method: apply the same operation (add, subtract, multiply, or divide by the same value) to both quantities simultaneously to cancel out shared terms, leaving a simpler comparison — just like solving an inequality.
মূল পদ্ধতি: উভয় রাশিতে একই ক্রিয়া প্রয়োগ করে সাধারণ পদ বাতিল করুন, তুলনা সহজ করুন।
Core Strategies
| Strategy | When to Use It |
|---|---|
| Simplify, don't fully solve | Cancel shared terms from both quantities using identical operations before doing any arithmetic. |
| Test multiple number types | When variables are involved with no stated constraints, test a positive integer, a negative number, a fraction, and zero — if the relationship changes, the answer is D. |
| Never multiply/divide by a variable | If a variable could be negative, multiplying or dividing by it can flip an inequality — avoid this until you know its sign. |
| Watch for "cannot be determined" being unavailable | If both quantities are specific numbers with no variables, the answer can never be D — one of A, B, or C must be correct. |
| Use given constraints fully | Information like "x is a positive integer" or "0 < y < 1" often rules out the number types that would otherwise force answer D. |
Worked Examples
| Quantity A | Quantity B |
|---|---|
| 3(x + 4) | 3x + 8 |
| Quantity A | Quantity B |
|---|---|
| x² | x |
(No constraints on x are given.)
Common Mistakes
- Assuming variables are positive integers by default: unless stated, a variable can be negative, zero, or a fraction — each can change the comparison.
- Multiplying both sides by a variable of unknown sign: this can silently flip the direction of the inequality without you noticing.
- Choosing D when specific numbers are given: if both quantities reduce to fixed numbers with no variables, D is never the correct answer — one relationship must hold.
- Stopping after testing only one number: a single test case that shows "A greater" doesn't rule out D; you must also test a case designed to break the pattern (negative, fraction, zero).
Your Turn
Compare each pair using simplification or number-testing. সরলীকরণ বা সংখ্যা পরীক্ষা করে প্রতিটি জোড়া তুলনা করুন।
Show the logic
Subtract 5x from both: A' = 7, B' = 3. A is always greater, regardless of x.
Show the logic
Any nonzero number squared is positive. A is always greater (A).
Show the logic
Expand A: x² + 6x + 9. Subtract x² + 9 from both: A' = 6x, B' = 0. If x > 0, A greater; if x < 0, B greater; if x = 0, equal. Answer: D.
Show the logic
For any fraction between 0 and 1, squaring makes it smaller (e.g., 0.5² = 0.25). A is always greater (A) — the constraint rules out the number types that would otherwise force D.
Show the logic
Average = (12+18+24)/3 = 54/3 = 18. Both specific numbers, no variables — D is not possible. The two quantities are equal (C).
Next guide: Arithmetic Shortcuts & Estimation. Apply this skill on Quant Practice Test 1.
পরের গাইড: পাটিগণিত শর্টকাট।